The length of time (T) in seconds it takes the pendulum of a clock to swing through one complete cycle is givenby the formula T=2pi square root of L divided by 32 where L is the length in feet, of the pendulum, and pi is approximately 22 divided by 7. How long must the pendulum be if one complete cycle takes 2 seconds?
T = 2(22/7)√(L/32) or
T = 2(22/7)(√L)/32 ???
Whichever equation it is, insert 2 for T and solve for L.
To find the length of the pendulum (L) when one complete cycle takes 2 seconds, you can use the formula:
T = 2π√(L/32)
Given that T is 2 seconds, the equation becomes:
2 = 2π√(L/32)
To solve for L, you need to isolate the variable L on one side of the equation.
1. Divide both sides of the equation by 2π:
2/(2π) = √(L/32)
This simplifies to:
1/π = √(L/32)
2. Square both sides of the equation to eliminate the square root:
(1/π)^2 = (L/32)
1/π^2 = L/32
To solve for L, multiply both sides of the equation by 32:
32/(π^2) = L
So, the length (L) of the pendulum must be approximately 10.21 feet when one complete cycle takes 2 seconds.
To find the length of the pendulum, we can rearrange the formula as follows:
T = 2π√(L/32)
We are given that T = 2 seconds. Plugging this in and simplifying the equation, we have:
2 = 2π√(L/32)
Divide both sides of the equation by 2π:
1 = √(L/32)
Square both sides of the equation:
1^2 = (√(L/32))^2
1 = L/32
Multiply both sides of the equation by 32:
32 = L
Therefore, the length of the pendulum must be 32 feet.